Low temperature (39 K – 298 K) kinetics study of the reactions of
C4H radical with various hydrocarbons observed in Titan’s atmosphere
Coralie Berteloitea, Sébastien D. Le Picarda*, Petre Birzaa, Marie-Claire Gazeaub, André
Canosaa, Yves Bénilanb, and Ian R. Simsa
a
Université de Rennes 1, Laboratoire PALMS, équipe Astrochimie Expérimentale
UMR CNRS-Université n° 6627,
Campus de Beaulieu, Bât. 11C, Université de Rennes 1,
35042 RENNES Cedex (France)
b
Universités Paris 12 et 7, Laboratoire Interuniversitaire des Systèmes Atmosphériques,
UMR CNRS-Université n° 7583
Faculté des Sciences et Technologie, 61 avenue du Général de Gaulle,
94010 CRETEIL Cedex (France)
Number of manuscript pages: 43 (including captions, tables and figures)
Number of figures: 11
Number of tables: 3
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Running head: This paper presents an experimental kinetics study at low temperatures of
reactions of C4H radical with various hydrocarbons relevant to Titan’s atmosphere. Possible
consequences of these results on the formation of large hydrocarbons are discussed as well as
comparison with rate coefficients used in the various photochemical models.
Corresponding author:
Sébastien LE PICARD
Laboratoire PALMS – UMR CNRS-Université n° 6627,
Equipe "Astrochimie Expérimentale",
Campus de Beaulieu, Bât. 11C, Université de Rennes 1,
35042 RENNES Cedex
FRANCE
-2-
Abstract
The reaction kinetics of the butadinyl radical, C4H, with various hydrocarbons detected in the
atmosphere of Titan (methane, ethane, propane, acetylene, ethene and methylacetylene) are
studied over the temperature range of 39 K – 298 K using the Rennes CRESU (Cinétique de
Réaction en Ecoulement Supersonique Uniforme) apparatus. Kinetic measurements were
made using the pulsed laser photolysis – laser induced fluorescence technique. The rate
coefficients, except for the reaction with methane, all show a negative temperature
dependence and can be fitted with the following expressions over the temperature range of
this study: kC2 H6 = 0.29
10-10 exp(-56.3 / T)
10-10 exp(-25.6 / T)
(T / 298 K)-1.24 cm3 molecule-1 s-1 ; kC3H8 = 1.06
(T / 298)-1.35 cm3 molecule-1 s-1; kC2 H2 =1.82
298 K)-1.05 cm3 molecule-1 s-1, kC2 H4 = 1.94
molecule-1 s-1, kCH3C2H = 3.21
10-10 exp(-9.5 / T)
10-10 exp(–47.2 / T)
10-10 exp(65.8/T)
(T /
(T / 298 K)-0.40 cm3
(T / 298 K)-0.82 cm3 molecule-1 s-1. These
expressions are not intended to be physically meaningful but rather to provide an easy way to
introduce experimental results in photochemical models. They are only valid over the
temperature range of the experiments. Possible channels of these reactions are discussed as
well as possible consequences of these results on the production of large molecules and hazes
in the atmosphere of Titan. These results should also be considered for the photochemistry of
Giant Planets.
Keywords: Titan, Atmospheres Chemistry, Organic chemistry, Experimental
-3-
Introduction
Polyynes are unsubstituted acetylene-like linear compounds with general formula C2nH2 [H–
(C C)n–H]. To date, only the simplest member of the series, C4H2 (H-C C-C C-H),
diacetylene, has been detected in the atmosphere of some planetary objects of our Solar
System: Jupiter (Gladstone et al., 1996), Uranus (Burgdorf et al., 2006), Saturn (de Graauw et
al., 1997) and its moon Titan (Kunde et al., 1981; Shemansky et al., 2005). Triacetylene (HC C-C C-C C-H), C6H2, has been identified in experimental simulations of Titan’s
atmosphere (de Vanssay et al., 1995). Photochemically reactive in the UV range, polyynes are
thought to be one of the possible precursors to the visible-absorbing haze materials present in
many planetary environments (Allen et al., 1980). Such compounds may play, therefore, a key
role in the chemistry of these planetary atmospheres.
Indeed in photochemical models of Jupiter (Gladstone et al., 1996; Lebonnois, 2005) (Moses
and Greathouse, 2005), Saturn (Moses et al., 2000) (Ollivier et al., 2000) and Titan (Wilson
and Atreya, 2004) (and references therein), polyynes are noteworthy for their role in the
formation of solid organic materials present in the atmosphere of these objects. Current
reaction networks modelling the chemistry involved in the evolution of such environments
describe the formation via a polymerization process starting from C2H2 :
(C2)nH2 + h
(C2)nH + H
(R1)
(C2)nH + (C2)mH2
(C2)(n+m)H2 + H
(R2)
With the aim to refine the description of such mechanisms in models, polyynes have been the
-4-
subject of various studies. However, except for the simplest of them, acetylene C2H2, these
compounds are not commercially available, and their synthesis and purification are more
difficult to perform as the length of the carbon chain increases. Furthermore, there is an
almost complete lack of quantitative data relating to larger polyynes due to their high thermal
instability and their inclination to polymerize at anything but the lowest partial pressures.
Nevertheless, absolute photoabsorption cross sections of some of these species at relevant
temperatures and over different ranges of wavelength have been determined in order to
predict the fate of those compounds under irradiation. Such work is essential for the
modelling of radiative transfer and photolysis rates. For example, for the two lightest
polyynes, butadiyne (C4H2) and hexatriyne (C6H2), also called diacetylene and triacetylene
respectively, absorption cross sections have been determined in the gas phase from 150 to 300
nm and at relatively low temperature (Benilan et al., 1995; Fahr and Nayak, 1994; Okabe,
1981; Shindo et al., 2003; Smith et al., 1998).
The reaction kinetics of the building up of complex long-chain carbon compounds has also
been studied. Most of the experimental research however, has been undertaken in the context
of combustion studies and, thus, has been conducted at temperatures of several thousands of
degrees (Krestinin, 2000) (and references therein). Only a very few rate coefficients have
been measured under conditions relevant for astrophysical environments, in particular at low
temperatures (Smith, 2006).
Focussing on the case of Titan’s atmosphere, a complex photochemistry that involves
polyynes among other hydrocarbons, takes place over a temperature range of 70—175 K, N2
being the background gas. In such a medium, the formation of C4H2 is confirmed by its
detection in the stratosphere from the analysis of the infrared spectra recorded by the Voyager
mission (Hanel et al., 1981; Kunde et al., 1981). Thus, to describe the mechanisms involved,
-5-
rate coefficients are required for reactions involving these species at low temperatures.
Relatively few data are available, being limited to the reactions of the C2H radical with
hydrocarbons with the work of Leone and co-workers employing laser photolysis and
transient infrared absorption spectroscopy in cooled cells down to 150 K (Hoobler and Leone,
1997; Hoobler and Leone, 1999) (Opansky and Leone, 1996a; Opansky and Leone, 1996b;
Pedersen et al., 1993), the work of Sims, Smith and co-workers employing laser-photolysis –
chemiluminescence detection in a CRESU (Cinétique de Réaction en Ecoulement
Supersonique Uniforme or Reaction Kinetics in Uniform Supersonic Flow) apparatus (Carty
et al., 2001; Chastaing et al., 1998), and the work of Leone and co-workers using the latter
detection technique in a pulsed CRESU apparatus (Goulay and Leone, 2006; Lee et al., 2000;
Murphy et al., 2003; Nizamov and Leone, 2004a; Nizamov and Leone, 2004b; Vakhtin et al.,
2001a; Vakhtin et al., 2001b).
Up to now, no data concerning the higher homologues were available in the literature as they
are very unstable compounds. In these circumstances, the only way for modellers to include
these reactions in their chemical schemes is to evaluate their rate coefficients from similar
reactions for which rates are available in the literature. Thus, arguing that higher polyyne
radicals are probably less reactive than C2H, rate coefficients for (C2)nH + hydrocarbon
reactions have been arbitrarily set to k((C2)nH) = 31-n k(C2H) by the authors of the first
photochemical models of Titan’s atmosphere (Lara et al., 1996; Toublanc et al., 1995; Yung
et al., 1984). More recently, the assumption adopted by (Wilson and Atreya, 2004) and
(Burgdorf et al., 2006; Hébrard et al., 2007) is that all (C2)nH reaction rates are equal to their
C2H analogues.
In spite of the use of the updated laboratory low temperature data, and thus the subsequent
improvement of the description of the chemistry of hydrocarbons, the mole fractions
-6-
estimated from the photochemical models do not well reproduce the observations (Hébrard et
al., 2007; Vinatier et al., 2007). For example, Table 1 shows that C4H2 is either overestimated
or underestimated compared to the concentration measured in Titan's atmosphere by ISO
(Infrared Space Observatory) or CIRS (Composite InfraRed Spectrometer onboard the Cassini
spacecraft orbiting Saturn) experiments at a given range of altitude (respectively 75—260 and
98—187 km). Moreover, the theoretical data for diacetylene, even those that take into account
the error bars for the kinetic rate coefficients, do not fit the very last profile obtained from
CIRS limb data (Vinatier et al., 2007). In fact, this is the case for the majority of unsaturated
hydrocarbons detected in Titan’s stratosphere. Since mean concentrations appear to be
controlled essentially by chemical rather than physical parameters (Lebonnois et al., 2001),
this discrepancy is probably due to a deficiency in the estimation of kinetic parameters
relating to the destruction or formation of C4H2 (Hébrard et al., 2007).
Another feature of Titan’s atmosphere is the presence of different layers of haze that give its
orange-brown colour when observed in the visible. The sources and mechanisms leading to
the formation of these hazes are still poorly understood. Photochemical formation of hazes
has been explored for more than twenty years. Although laboratory simulations have shown
that formation of aerosol particles could involve photolysis of acetylene (C2H2), ethylene
(C2H4), and hydrogen cyanide (HCN), the difficulty of performing simulations of these
processes under the conditions of the atmosphere of Titan makes those results quite
speculative. The possible roles of polyynes (Yung et al., 1984), nitriles (Banaszkiewicz, 2000)
and more recently aromatics (Lebonnois et al., 2002; Wilson and Atreya, 2003) have been
studied in various models. The scarcity of kinetic measurements however, especially under
the physical conditions of the atmosphere of Titan, makes these analyses uncertain.
We suggest that reactions of the type [R2] could play a role in the formation of long
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polyacetylenic chains and large molecules. The kinetics study at low temperatures of C4H
radical reactions with various hydrocarbons among the most abundant observed in Titan’s
atmosphere (CH4, C2H2, C2H4, C2H6, CH3C2H and C3H8) that we present here should help
modellers to assess this assumption.
2. Experimental technique
The CRESU technique which is now well established for the study of gas phase reaction
kinetics at very low temperatures (Dupeyrat et al., 1985; Sims et al., 1994), has been used in
the present study. CRESU is a French acronym standing for Cinétique de Réaction en
Ecoulement Supersonique Uniforme which can be translated as Reaction Kinetics in Uniform
Supersonic Flow. Here, we concentrate on those features of our experiments which are
specific to kinetic experiments on the reactions of C4H radicals.
In the CRESU technique, low temperatures are achieved via the isentropic expansion of a
buffer gas through a Laval nozzle. Each nozzle employed provides an axially and radially
uniform supersonic flow at a particular temperature, density and velocity for a given buffer
gas. The relatively high density of the supersonic flow (1016—1017 cm-3) ensures frequent
collisions, thus maintaining thermal equilibrium. All these properties are conserved in the
core of the supersonic flow over a typical distance of a few tens of centimetres along the flow
corresponding to a hydrodynamic time of several hundreds of microseconds. The Laval
nozzle is mounted on a reservoir kept at room temperature into which the buffer gas, the C 4H
precursor molecule and the reagent gases were injected.
C4H radicals were created by the pulsed laser photolysis of diacetylene, C4H2, using the 248
nm radiation of a KrF excimer laser (Lambda Physik, LPX 200). The beam from this laser
entered the CRESU chamber through a Brewster angle window and propagated counter to the
gas flow.
-8-
C4H2 was synthesized by dehydrochlorination of 1,4-dichloro-2-butyne (C4H4Cl2)(Khlifi et
al., 1995). Given the high instability of diacetylene, only small amounts were synthesized
before a series of kinetic experiments. Once synthesized, C4H2 was mixed with helium gas in
a 20 L glass vessel at a total pressure of ca. 1.2 bar. He-C4H2 mixture was injected into the
reservoir of the CRESU chamber using very small flows of the order of a few standard
cm3min-1.
C4H radicals were detected by laser induced fluorescence (LIF) using a 2
band type of the B 2
i
X 2
2
vibronic
electronic system. Laser radiation at a wavelength of ca. 408
nm was generated using the frequency doubled output of a Nd:YAG laser (Continuum,
Powerlite Precision II) to pump a dye laser (Laser Analytical Systems, LDL 20505) operating
with Styryl 9M dye (Sigma Aldrich) in methanol, the output of which was frequency doubled
in a BBO crystal. The linewidth of the UV laser was measured with a wavemeter
(HighFinesse/Angstrom, WS-7R) to be 0.24 cm-1. This probe laser entered the CRESU
chamber and gas reservoir through two quartz Brewster angle windows and passed through
the Laval nozzle throat and down the gas flow along its axis counter to the direction of the
photolysis beam. Fluorescence from C4H ( B 2
i
) was collected at right angle to the laser
propagation direction using an optically fast collection system, and detected with a
photomultiplier tube (Thorn EMI, 9813 QSB) through a low-pass glass filter (Schott, GG
435). The signal from the PMT was recorded by a gated integrator and a boxcar averager
(Stanford Research Systems) and transferred to a PC via an IEEE interface (Stanford
Research Systems, SR 245) controlled by data acquisition software. The time delay between
the pump and probe beams, which was scanned to generate decay traces, was controlled by a
four-channel delay/pulse generator (Stanford Research Systems, DG535), which was also
controlled by the same data acquisition software via an IEEE interface.
-9-
A typical LIF decay trace for C4H at 52 K is shown in Fig. 1. As can be seen, a finite rise time
was observed for the C4H LIF signal. This was taken as resulting from collisional relaxation
of C4H formed in electronic and/or rotationally excited states. Indeed, the first excited
electronic state of C4H, A 2
, is predicted to lie very close to the ground state, with
theoretical estimations varying from 70 cm-1 to 565 cm-1 (Woon, 1995). Photoelectron
spectroscopy experiments of C4H– anions allowed the authors to give an upper limit for the
energy of the A 2
state: Neumark and co-workers (Taylor et al., 1998) gave an upper value
of 468 cm-1, while more recent experiments by Pino et al. (Pino et al., 2002) were consistent
with an A 2
state lying at a lower energy of ca. 160 cm-1 above the X 2
ground state,
which is a value cited as a private communication by Endo and co-workers in the paper by
Neumark and co-workers (Taylor et al., 1998). In order to avoid contamination of the data, all
nonlinear least-squares fits of the exponential decays of the LIF signals were started after this
rise corresponding to electronic and/or rotational relaxation of C4H was complete, and
pseudo-first-order decay times were kept at least ten times longer than this rise time. For a
given temperature, LIF scans were then taken for different reagent concentrations in the usual
way in order to construct a kinetic plot from which the second-order rate coefficient could be
extracted. Fig. 2 shows a second-order plot for C4H + C2H6 at 52 K. Measurements at room
temperature were performed in the CRESU apparatus as previously described (Sims et al.,
1994).
Hydrocarbon reagents were mixed with the buffer gas before passing into the reservoir and
expanding through the Laval nozzle. CH4 (99.995%), C2H4 (99.95%), C2H6 (99.995%), C3H4
(methyl acetylene) (96%) and C3H8 (99.95%), all from Air Liquide, C2H2 (99.6%, AGA) and
carrier gas (N2 and Ar; Air Liquide, 99,995%) were taken directly from cylinders and
regulated by means of calibrated MKS mass flow controllers. Knowledge of the total gas
- 10 -
density along the flow, and of the individual gas flow rates, allowed the hydrocarbon
concentrations in the supersonic flow to be calculated.
3. Results
3.1 C4H spectra
To our knowledge the most recent spectroscopic work on neutral C4H was published by Endo
and co-workers (Hoshina et al., 1998; Pino et al., 2002). In their paper, (Hoshina et al., 1998)
present and analyse twenty vibronic bands of C4H observed by laser induced fluorescence
(LIF) in the 24000 – 25000 cm-1 region, corresponding to the range of wavelengths 400 to 416
nm. Figure 3 shows a survey spectrum obtained in our experiment at 52 K for a time delay
between the photolysis laser and the probe laser of 20 µs over the same wavelength range.
Most of the vibronic bands observed by Endo and co-workers (Hoshina et al., 1998) are also
present in our spectrum, only the weakest of them are absent. We did not, however, see any of
the C3 features which were observed by Endo and co-workers probably as a result of their use
of a discharge source, in contrast to the more specific photolytic source of C4H radical used in
this study. We have performed a theoretical simulation of the entire band system using the
spectroscopic parameters determined by (Hoshina et al., 1998). Some bands also present in
the spectra of Endo and co-workers clearly show up here. They cannot be attributed to C3
since it is not present in detectable amount in our spectra (less than 1% relative to C4H). A
complete reanalysis of the C4H band system will be presented elsewhere. To perform our
kinetic measurements we used the band at 24490.8 cm–1 referred to as the [J] band
(corresponding to a transition from the ground state to the B 2
i
3
5
excited state) by
Endo and co-workers, as this band is one of the most intense and suffers least from overlap
with other bands. Figure 4 shows this band observed in our experiment at 52 K, as well as a
simulation calculated using the spectroscopic parameters determined by (Hoshina et al., 1998)
- 11 -
except for a rotational constant of the upper state B'eff = 0.1512(1) cm-1 and spin splitting
constant Gamma' = 0.009(1) cm-1.
The band is quite well reproduced, apart from the
perturbed lines as already noticed by (Hoshina et al., 1998), with a Voigt profile using a
resolution of 0.08 cm-1.
To obtain the kinetic measurements presented in the next section, we used the R-band head of
the transition, which is the most intense part of this spectrum, as can be seen in Fig. 4.
3.2 Kinetic measurements
Our experimentally measured rate coefficients are summarized in Table 2 which also reports
the main flow conditions for each study. The quoted uncertainties comprise statistical errors
calculated as the standard error obtained from the fit of the second-order kinetic plot
multiplied by the appropriate Student’s t factor for the 95% confidence limit combined with
an estimate of possible systematic errors. The latter are essentially due to flow control
inaccuracies or inaccuracies in the determination of the buffer gas total density. Every effort
was made to minimize these and we estimate that they do not exceed 10%.
In Figures 5 to 9, the rate coefficients k(T) that we obtained are displayed as a function of the
temperature on log-log plots. Results of the fittings of the data are presented in Table 3, using
the equation k(T) = A exp(– / T)(T / 298 K)n and the resulting values of A,
and n are given
with their associated statistical uncertainties. We emphasise that these expressions are only
valid over the temperature range 39–300 K. They are not intended to be physically
meaningful but rather to provide an easy way to introduce experimental results in
photochemical models with a good level of confidence, as these fits do not generally deviate
too much from our measurements.
In every case, with the exception of methane, the rate coefficients for the reactivity of
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hydrocarbons with C4H are close to the collisional rates and show slight negative temperature
dependences. In the case of methane, which reacts much more slowly, we were not able to
obtain any rate coefficient below 200 K. The measurements are limited by both the length and
therefore the duration of the supersonic flow, as well as the maximum concentration of
hydrocarbon possible without either perturbing the supersonic flow, or causing condensation.
These limitations preclude the determination of rate coefficients slower than ~ 5
10-13 cm3
molec-1s-1.
Most of the rates were obtained using nitrogen as a buffer gas, with the exception of the
measurements at 50 K and some of the measurements at 300 K that were obtained using argon
as a buffer gas. Considering the temperature dependences k(T), results derived in argon are
fully consistent with those obtained in nitrogen, showing no effect of the nature of the buffer
gas (N2 or Ar) on the rate coefficients measured. In addition, at 50 K we performed kinetic
experiments for all gases with nozzles giving two different densities: 0.52
1.01
1017 cm-3 and
1017 cm-3. In both cases the rates obtained were the same, within the uncertainty of our
experiments. At 300 K, measurements with methane were also performed at two densities,
0.68
1017 cm-3 and 2.07
1017 cm-3 respectively, and the rate coefficients were found to be
similar. These results indicate that either all these reactions are bimolecular or that they were
obtained in the high pressure limit of a termolecular process, the third body being the buffer
gas (N2 or Ar).
4. Discussion
4.1 Temperature dependences and possible products of the reactions
In this subsection, we comment the temperature dependences observed in our experiments and
give some insights on the possible products formed by these reactions. More details on the
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chemistry of these reactions, and others involving C4H with a larger number of hydrocarbons
will be given elsewhere (Berteloite et al., in preparation).
Reaction of C4H with methane (CH4), ethane (C2H6) and propane (C3H8)
The rate coefficients of the reaction of C4H with methane (Fig. 5) show a slightly positive
temperature dependence as observed by (Opansky and Leone, 1996a) in the case of the
reaction of C2H with methane, with almost the same
rate coefficients. This behaviour
indicates the presence of a small barrier along the minimum energy path for the reaction.
Fitting their results with an Arrhenius type function, Opansky and Leone were able to derive
an activation energy of 4 kJ mol-1 for the reaction C2H + CH4. As we only have data at two
temperatures, 298 K and 200 K, it would be too risky to derive such a barrier in our case. By
analogy with the reaction of C2H with methane, we believe this reaction to proceed more
likely via hydrogen abstraction, C4H2 and CH3 being the two subsequent products. Given the
high mixing ratio of CH4 in the stratosphere of Titan, ca. 1.4%, this reaction would represent
an important way of recycling diacetylene. The production of the methyl radical, CH3, is also
worthy of note, as the recombination of two methyl radicals will form ethane, the second most
abundant hydrocarbon in the atmosphere of Titan.
In the cases of ethane and propane (Fig. 6 and 7), the rate coefficients present negative
temperature dependences, the rate coefficient being larger for propane than for ethane. This
negative temperature dependence is consistent with reactions proceeding through potential
energy surfaces with no or very small energy barriers. The increase of the reactivity with the
number of carbons in the alkanes has already been observed in other studies (Murphy et al.,
2003; Sims et al., 1993) and is probably due to the increasing number of primary and
secondary hydrogen available in the co-reactant of C4H. As in the case of methane, we believe
the hydrogen abstraction to be the most probable channel, forming C4H2 and C2H5 in the
- 14 -
reaction with ethane, and C4H2 and C3H7 in the reaction with propane. All the reactions with
alkanes presented here are therefore likely to recycle C4H2 and produce alky radicals.
Reaction of C4H with acetylene (C2H2)
As for reactions involving large alkanes, we found the rate coefficient for C4H + C2H2 to
increase when the temperature is lowered (Fig. 8), with rate coefficients larger than those for
the reactions with alkanes. This indicates the absence of an energy barrier along the minimum
energy path for the reaction. The higher reactivity of acetylene compared to the alkanes is
probably due to the presence of
electrons in C2H2. The most likely mechanism could be the
addition of the electrophilic C4H to the
orbital of C2H2, thus forming a C6H3 intermediate
which could subsequently undergo a C-H bond fission. This reaction mechanism would be
quite similar to those of the analogous C2H + C2H2 (Stahl et al., 2002) and CN + C2H2 (Huang
et al., 2000) reactions. Interestingly, the structures of some C6H3 isomers have been recently
calculated at the B3LYP/6-311G(d,p) level of calculations (Guo et al., 2007). The isomer
identified as p3 in that paper has the correct properties to be the addition intermediate:
according to the above mentioned calculations, the formation of the C6H3 addition
intermediate from C4H and C2H2 would be exothermic by ca. 250 kJ mol-1, thus reinforcing
the suggestion that an addition mechanism is possible.
The main products would be therefore, C6H2 and H. This is obviously a very interesting
channel for the atmospheric photochemistry of Titan, as it forms the next polyyne after C4H2,
triacetylene (C6H2), so increasing the chain length of the hydrocarbon. The formation of other
products however, following the dissociation of the short-lived intermediate complex, C6H3‡,
cannot be completely excluded. Furthermore, the possibility of an abstraction process, leading
to the formation of C4H2 and C2H can not be ruled out as this channel is exothermic by ca.
100 kJ mol-1. It is worth noting that this abstraction channel was not open at low temperature
- 15 -
in the case of C2H + C2H2 and CN + C2H2 as these reactions are thermoneutral and
endothermic respectively.
Reactions of C4H with ethene (C2H4) and methylacetylene (C3H4)
For these two reactions we found a similar temperature dependence (Fig. 9 and 7) as for the
reaction with acetylene, with slightly larger rate coefficients. Again, these reactions are likely
to proceed through the addition of the electrophilic C4H radical to the multiple bond of
ethene, C2H4, or methylacetylene, CH3C2H, immediately followed by the formation of
fragments. The hydrogen displacement channel, giving the radical C6H4 in the case of ethane,
and C7H4 in the case of methylacetylene, seems the most probable reaction mechanism,
especially if we consider the results of (Stahl et al., 2002) on the dynamics of C2H with
hydrocarbons in crossed beam experiments. Other channels however, in particular an H
abstraction mechanism similar to that occurring with saturated hydrocarbons, cannot be ruled
out.
4.2 Destruction of C4H radical by hydrocarbons in the atmosphere of Titan
In order to evaluate the efficiency of each reactant as a destruction route of C4H the ratio
of the characteristic time,
of CH4,
CH4,
X,
for the reactions of C4H with these hydrocarbons relative to that
can be calculated using the observed abundances and the rate coefficients
obtained in our study. We can easily show that:
CH 4
X
nX k X
nCH4 kCH4
where nX / nCH4 is the relative abundance of hydrocarbon X with respect to CH4 and kX and
kCH4 are the rate coefficients for the reaction of C4H with hydrocarbon X and CH4
respectively. Values greater than say 0.1 for this ratio of characteristic times will indicate that
- 16 -
hydrocarbon X will play a significant role in the destruction of C4H and therefore must be
taken into account in the photochemical scheme.
The Cassini-Huygens mission is providing very interesting new data with respect to the
composition of the atmosphere of Titan (Flasar et al., 2005; Niemann et al., 2005; Shemansky
et al., 2005; Teanby et al., 2006; Teanby et al., 2007; Vinatier et al., 2007; Waite et al., 2005)
from which it is possible to obtain a new description of the concentration profiles with respect
to the altitude.
Figure 10 is an attempt to summarize these data over the altitude range 120 – 1200 km
for the hydrocarbons of interest here. Data in the stratosphere were taken from (Flasar et al.,
2005) and (Vinatier et al., 2007). Flasar et al. measured abundances of several species in the
stratosphere as a function of latitude using the CIRS apparatus of the Cassini orbiter during
fly-bys T0 and Tb. Methane abundance (1.6±0.5 %) was obtained over the altitude range 80—
140 km whereas other hydrocarbon abundances were derived between 140 and 180 km
(Flasar et al., 2005;Waite et al., 2005). Mean abundances with respect to latitude were derived
from their data and plotted in Figure 10 at ~180 km. Another study by (Niemann et al., 2005)
based on the GCMS instrument (Gas Chromatograph Mass Spectrometer) show that methane
was uniformly mixed with a mole fraction of 1.41±0.07 % in the stratosphere. More recently,
(Vinatier et al., 2007) analysed spectra obtained with CIRS during fly-bys Tb (15° S) and T3
(80° N) from which vertical profiles were derived for a series of hydrocarbons in the altitude
range 100-460 km (Tb fly-by) and 170-495 km (T3 fly-by). For clarity, in Figure 10 we have
only included their results corresponding to the low latitudes Tb fly-by. Data from 450 km to
1000 km were derived from the measurements by (Shemansky et al., 2005) who obtained the
densities of a variety of molecules using the Cassini UVIS (Ultraviolet Imaging Spectrometer)
experiment. Finally, data at ~1200 km were extracted from the work by (Waite et al., 2005)
- 17 -
who derived abundances from the INMS (Ion Neutral Mass Spectrometer) apparatus. Note
that the abundance taken for propane is an upper limit whereas for ethene we chose the lowest
value indicated in their paper.
In the altitude range that we are considering here, the temperature varies from about 150
to 200 K. Over this range our rate coefficients do not vary significantly with temperature and
therefore we made our analysis taking a mean value for each hydrocarbon: kC2 H2 = 2.2 10-10
cm3 molecule-1 s-1; kC2 H4 = 3.0 10-10 cm3 molecule-1 s-1; kC2 H6 = 0.5 10-10 cm3 molecule-1 s-1;
kCH3C2H = 3.5 10-10 cm3 molecule-1 s-1and kC3H8 = 1.5 10-10 cm3 molecule-1 s-1. For methane, as
already mentioned, we were not able to study its reactivity below 200K. Considering that this
process is very slow and that our data indicate a reduction of the rate coefficient when the
temperature is lowered from 300 K to 200 K, we have arbitrarily chosen to take a rate
coefficient slightly lower (and probably too high at 150 K) than our measurement at 200 K for
the present analysis: kCH 4 = 6
10-13 cm3 molecule-1 s-1.
Using these assumptions it is then possible to calculate for every altitudes the ratio
CH4/ X
and therefore to analyze the possible impact of each hydrocarbon in the destruction
process of C4H. As can be seen in Figure 11, at altitudes greater than 600 km, excepting
propane and methyl acetylene for which no data are presently available, the ratio
CH4/ X
is
much greater than 1 indicating that the destruction of C4H by C2H2, C2H4 and C2H6 is more
efficient than that by methane. This is especially striking in the ionosphere within 800 and
1000 km. These conclusions were also drawn in a recent study of the reactivity of the C 2
radical with hydrocarbons (Canosa et al., 2007). In that study however, the effect was not as
striking as in the present work because reactivity of C2 + CH4 was found to be about 20 times
higher than that of C4H + CH4. At 1200 km, reactions with C2H2 and C2H4 are still dominant
- 18 -
whereas the reaction with ethane becomes less efficient than methane although still significant
(
CH4/ C2H6
~0.5). It is also worth stressing that the contributions of propane and methyl
acetylene increase significantly with respect to lower altitudes (
CH4/ C3H4
CH4/ C3H8
~ 0.06 and
~0.1 respectively) although their reaction with C4H still remains much less efficient
than that of C2H2 and especially C2H4 as a destruction source of C4H.
In Titan's stratosphere, abundances of hydrocarbons are much smaller and therefore
destruction reactions of C4H by hydrocarbons are no longer dominant with respect to
methane. It is worth noting however that
CH4/ X
is close to 0.1 for C2H2 and C2H6 which are
then significant destruction sources of C4H in this zone. On the other hand, propane, ethene
and methyl acetylene will play a minor role as the ratio
CH4/ X
is only a few % or even less
for these species. As mentioned above the choice of the rate coefficient kCH4 may be too high
at 150 K. A rough extrapolation of our measurements down to 150 K would give a rate
coefficient of about kCH4(150K) = 4 10-13 cm3 molecule-1 s-1 which is not significantly
different from the adopted value. Furthermore, a lower value would even more emphasize the
impact of other hydrocarbons than the present analyses and will not change our conclusions.
Considering the data obtained during the T3 fly-by, one can observe that the derived
abundances were generally found to be larger than those obtained from the Tb fly-by. This
essentially reflects the polar enrichment in these high latitudes conditions resulting from
circulation in winter time. Although they are far from common in Titan's atmosphere it is
interesting to point out that the efficiency of C2H2 in the destruction of C4H is significantly
greater than in the equatorial area and increases with altitude. At ~460 km the ratio
CH4/ C2H2
becomes close to 0.5. The effect of these peculiar atmospheric conditions for other molecules
is either insignificant (C2H6, C3H8) or not sufficient (CH3C2H, C2H4) to modify the
conclusions that we indicated for the Tb fly-by data.
- 19 -
4.3 Comparison with rate coefficients used in various photochemical models
Since the pioneer model of the atmosphere of Titan by Yung and coworkers in 1984(Yung et
al., 1984), various photochemical models have been developed, incorporating the chemistry,
some of them also adding the transport of species in the atmosphere. The choice of the
chemical scheme, and the quality of the rate coefficients used have been improved over the
years, often taking into account the latest laboratory measurements when available. Figures 5
to 9 show the rate coefficients used in the various photochemical models (Lara et al., 1996;
Lebonnois et al., 2001; Toublanc et al., 1995; Wilson and Atreya, 2004; Yung et al., 1984) for
the reactions of C4H with hydrocarbons. It can be seen that differences between predictions
used and the measurements we made can reach several orders of magnitude, especially at the
lowest temperatures. It is worth noting that in some of these models (Yung et al., 1984),(Lara
et al., 1996),(Toublanc et al., 1995), authors followed the recommendation by (Yung et al.,
1984) to adjust arbitrarily the rate coefficients of reactions involving polyacetylene radicals to
those involving C2H using the following formula: k((C2)nH) = 31-n k(C2H). In the most recent
of these models however (Wilson and Atreya, 2004), the authors used the experimental results
obtained at low temperatures by Leone and co-workers (Hoobler and Leone, 1997; Hoobler
and Leone, 1999; Lee et al., 2000; Murphy et al., 2003; Nizamov and Leone, 2004a; Vakhtin
et al., 2001a; Vakhtin et al., 2001b) and Smith and co-workers (Carty et al., 2001; Chastaing
et al., 1998) for the analogous reactions with C2H in order to derive an upper limit for the
production of polyacetylene polymers. It is worth noting that if the temperature dependence is
about the same as for the reactions with C4H, the absolute rate coefficients we measured are
always larger by a factor of two to four, with the exception of reactions with methane.
- 20 -
4.4 The role of C4H radical for the formation of big molecules and haze
As mentioned in the Introduction, photochemical sources of hazes have been explored in
various models and recently Wilson et al. (Wilson and Atreya, 2003) have considered the role
of polymerization of pure polyacetylenes in the formation of the hazes as suggested in 1980
by Allen et al. (Allen et al., 1980). In their photochemical model, the first step for the growth
of polyacetylenic chains is given by the reaction
C2H + C2H2
C4H2 + H
whose rate coefficient has been measured at low temperatures by Chastaing et al. (1998). The
chain-lengthening process is therefore considered to be continued through the photolysis of
C4H2 forming polyacetylene radicals: C4H, C6H and C8H. As mentioned in section 4.2, the
reaction of C4H with acetylene is very likely to form efficiently triacetylene, C 6H2. Reactions
of polyacetylene radicals with C4H2, C6H2 and C8H2 are proposed by Wilson and Atreya
(Wilson and Atreya, 2003) to lead to the formation of polyacetylene polymers.. In their
model, the rate coefficients for all these reactions were taken as equal to that of C2H + C2H2
as measured by Chastaing et al. (Chastaing et al., 1998) and Leone and co-workers (Vakhtin
et al., 2001a). Our results show however that the rates constants for C4H + C2H2 are actually
about two times faster. Finally, Wilson et al. (Wilson and Atreya, 2003) found the
contribution of polyacetylenes to be insignificant compared to the channel involving
aromatics for the formation of hazes and it would be worth to know how our new results
could affect their conclusions. It has to be mentioned however, that most of the kinetics of
aromatics considered in this photochemical model have not been studied experimentally at
low temperature so far, making these results still quite speculative.
- 21 -
The role of metastable states of diacetylene, C4H2*, in the formation of large molecules in
Titan’s atmosphere has also been explored in the 1990’s by Zwier and co-workers ((Zwier
and Allen, 1996)and reference therein). More specifically, Zwier and Allen (Zwier and Allen,
1996) compared the efficiency of C4H2* reactions with free radicals as routes for forming
large hydrocarbons and nitriles. The main reactions involved in their chemical scheme were
the reactions of C4H2* with unsaturated hydrocarbons, the reactions of C2H with C4H2, CH4
and C2H2 and the reactions of C4H with C2H2 and CH4. At that time however, none of these
reactions had been studied at low temperatures, and the rate constants for C2H and C4H
reactions were taken from the photochemical model of (Toublanc et al., 1995) and reference
therein. As can be seen on Fig. 8, our experimental results differ from those used by
(Toublanc et al., 1995) by an order of magnitude considering for instance the reaction C4H +
C2H2. The role of the metastable states of C4H2* in the formation of large molecules in Titan’s
atmosphere should be therefore, reconsidered.
5. Conclusion
The work presented here is, to our knowledge, the first ever experimental reaction kinetics
investigation involving the radical C4H. Rates of the reactions between C4H and methane
were found to be very close to those of C2H with methane, with a small energy barrier along
the minimum energy path for the reaction. For all the other reactions studied here, the rate
coefficients are very fast (k
10-10 cm3molecule-1s-1) with k increasing when the temperature
is lowered. These reactions are therefore dominated by long range dispersion forces and
proceed on a potential energy surface with no barrier or a small barrier in the entrance
channel. The rate coefficients are all larger than those found for reactions of C2H with the
same hydrocarbons. These new rate coefficients should therefore be included in future
- 22 -
photochemical models of the atmosphere of Titan and of other planets containing methane.
Reactions with alkanes are likely to recycle C4H2 while other reactions could form various
products of interest as for instance triacetylene, C6H2 in the case of the reaction involving
acetylene. For the other reactions involving unsaturated hydrocarbons (C2H2, C2H4, CH3C2H),
a short-lived addition complex is likely to be formed, that decomposes to give various
products with H-atom elimination being probably the dominant channel. The high enthalpy
of formation of C4H offers however, many possibilities for the products, more than is the case
for C2H or CN radicals, and therefore the formation of radicals leading to larger molecules,
such as PAHs for instance. The role of these products in the formation of big particles and
hazes should be further explored. These kinetics results therefore, even measured at low
temperatures (40 K – 298 K), could be also of interest for chemical schemes leading to the
formation of soot in combustion (Krestinin, 2000).
Acknowledgements
We thank the ―Programme National de Planétologie‖, the ―Programme National Physique et
Chimie du Milieu Interstellaire‖, the ―Région de Bretagne‖, ―Rennes Métropole‖ and the
European Union (RTN Network "Molecular Universe", contract MRTN-CT-2004-512302)
for support. I.R.S. gratefully acknowledges support for this work from the European Union
via the award of a Marie Curie Chair (Contract MEXC-CT-2004-006734, ―Chemistry at
Extremely Low Temperatures‖). We are also grateful to Dr. Nadia Balucani for helpful
discussions on the dynamics of the reactions presented in this paper.
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hydrocarbons in Titan's atmosphere. Icarus. 123, 578-583.
- 27 -
TABLE 1. Comparison between mixing ratios observed by ISO (2003) and the Cassini
CIRS instrument (2005) with various photochemical models.
Model
Compound
Altitude
(km)
Yung
et al.
(1984)
Toublanc
et al.
(1995)
125
2.0x10-4
1.2x10-5
C2H2
125
4.3x10-5
2.2x10-6
C3H8
105
4.2x10-6
2.8x10-7
C2H4
125
3.1x10-7
105
C2H6
CH3C2H
C4H2
105
Lara
et al.
(1996)
8.7x10-6
3.0x10-6
(a)
1.0x10-7
Observation
Lebonnois et
al.,
(2001) ;
(2002)
Wilson &
Atreya
(2004)
Nom. with
fractal :
Mie haze
2.7x10-6
1.9x10-6
(b)
2.4x10-7
3.2x10-9
8.3x10-8
2.1x10-8
9.5x10-7
1.4x10-8
2.3x10-11
9.8x10-10
1.6x10-10
6.8x10-9
4.7x10-9
3.9x10-9
(c)
5.8x10-6
1.2x10-5
1.9x10-6
1.1x10-6
6.3x10-8
2.8x10-7
9.4x10-9
1.5x10-8
1.8x10-9
6.6x10-10
6.2x10-10
1.9x10-9
ISO
CIRS
Alt. 75-260 km
Coustenis et al.
(2003)
Alt. 98-187 km
10°S
Flasar et al.
(2005)
2.0
0.8 10-5
0.3
1.8 -0.45
10 -5
5.5
0.5 10-6
0.1
3.0 - 0.2
10 -6
2.0
1.0 10-7
5.9- 22.1 10-7
1.2
0.3 10-7
0.7
2.1- 0.2
10 -7
1.2 0.4 10- 8
2.0
0.5 10-9
1
9.0 - 1.5
10 -9
0.3
1.3 - 0.2
10 -9
(a) mixing ratio at 130 km, (b) mixing ratio at 105 km, (c) mixing ratio at 125 km
- 28 -
TABLE 2. Rate coefficients measured at different temperatures for the reactions of
C4H with CH4, C2H2, C2H4, C2H6, C3H8 and CH3C2H.
Temperature (K)
39
52
83
145
200
300
300
Carrier gas
Total density
(1016 molec cm-3)
N2
Ar
N2
N2
N2
Ar
N2
3.3
10.3
4.9
9.2
5.83
25
21.5
Range of reactant gas density (1012 molec cm-3)
CH4
1.103-1.104
350-3500
C2H2
3-32
13-77
2.5-47.5
10-110
13-264
C2H4
3-33
14-137
4-26
10-110
25-386
C2H6
13-134
10-107
19-192
89-448
215-1039
C3H8
7-27
7-79
8-7
13-66
78-728
CH3C2H
2-14
5-33
3-34
8-79
14-164
Rate coefficient (10-10 cm3 molec-1 s-1)
0.77±0.12
10-2
CH4
2.13 ± 0.2
10-2
C2H2
2.57 ± 0.24 a
3.88 ± 0.14
2.74 ± 0.08
2.54 ± 0.20
1.54 ± 0.06
C2H4
5.57 ± 0.32
4.84 ± 0.08
3.19 ± 0.43
3.27 ± 0.12
1.8 ± 0.07
C2H6
1.75 ± 0.04
1.81 ± 0.02
0.78 ±0.04
0.58 ± 0.03
0.41 ± 0.02
C3H8
3.70 ± 0.22
4.15 ± 0.07
2.72 ± 0.3
1.88 ± 0.19
1.03 ± 0.42
CH3C2H
4.93 ± 0.58
5.66 ± 0.21
5.04 ± 0.61
4.13 ± 0.33
2.80 ± 0.25
a
Uncertainties (here and throughout the tables) are calculated using the statistical error evaluated on the second
order plot via the Student’s t factor (95%). A systematic error of 10% was added to take into account
contribution from possible systematic errors.
- 29 -
TABLE 3. Fit parameters (A, , n) of our kinetic data according the following equation
T
T
298 K
the range T = 39–300 K.
k2 nd
A exp
for each reagent C2H2, C2H4, C2H6, C3H8 and CH3C2H, in
estimated uncertainty a /
10-10
3
cm molecule-1 s-1
A/
cm3 molec-1 s-1
/
K
C2H2
1.82
65.79
-1.06
0.75
C2H4
1.95
-9.52
-0.40
0.65
C2H6
0.29
25.58
-1.24
0.37
C3H8
1.06
56.27
-1.35
0.48
CH3C2H
3.21
47.20
-0.82
0.29
10-10
a
n
Corresponds to 2σ with
( k2 nd exp k2 nd fit )2
number of experimental point s
- 30 -
n
Figure captions
2
Figure 1. Decay of C4H ( 2
) LIF signal at 52.3K in the presence of C2H6 ([C2H6] =
14
-3
0.43 10 molecule cm ) and Ar buffer ([Ar] = 10.3 1016 molecule cm-3), fit to a singleexponential function.
Figure 2. Second order plot for the reaction of C 4H + C2H6 at 52.3K in Ar, leading to a value
for the second-order rate coefficient of k = (1.81 ± 0.02) 10-10 molecule-1 cm3 s-1.
Figure 3. LIF spectrum survey at 52.3K of products of C4H2 photolysis at 248 nm. Simulation
was calculated using a temperature of 50 K, a Voigt profile of 0.08 cm -1 (FWHM) and
spectroscopic parameters derived by (Hoshina et al., 1998). Transitions [A-W] belong to the
C4H radical according (Hoshina et al., 1998).
2
Figure 4. LIF spectrum of a 2
[J] band of C4H. Observed spectrum is obtained at 52.3
K, simulation was calculated using a temperature of 50 K and a Voigt profile of 0.08 cm-1
(FWHM).
Figure 5. Rate coefficients for the reaction of C4H with CH4 as a function of temperature,
displayed on a log-log scale. The filled circles show the experimental results obtained in this
work. The dashed lines represent equations used for this reaction in various photochemical
models of the atmosphere of Titan. The long dashed line represents data from (Wilson and
Atreya, 2004), the medium dashed line from (Toublanc et al., 1995), the dotted line from
(Lara et al., 1996) and the dash-dotted line from (Yung et al., 1984).
Figure 6. Rate coefficients for the reaction of C4H with C2H6 as a function of temperature,
displayed on a log-log scale. The filled triangles down show the experimental results obtained
in this work and the bold solid line shows the fit to these data. The other dashed lines
represent equations used for this reaction in various photochemical models of the atmosphere
of Titan. The long dashed line represents data from (Wilson and Atreya, 2004), the medium
dashed line from (Toublanc et al., 1995), the dotted line from (Lara et al., 1996) and the dashdotted line from (Yung et al., 1984).
Figure 7. Rate coefficients for the reaction of C4H with respectively C3H8 and CH3C2H as a
function of temperature, displayed on a log-log scale. The filled squares show the
experimental results obtained in this work for C3H8 and the bold solid line shows the fit to
these data. The filled triangle down show the experimental results obtained in this work for
CH3C2H and the solid line shows the fit to these data.
- 31 -
Figure 8. Rate coefficients for the reaction of C4H with C2H2 as a function of temperature,
displayed on a log-log scale. The filled circles show the experimental results obtained in this
work and the bold solid line shows the fit to these data. The other dashed lines represent
equations used for this reaction in various photochemical models of the atmosphere of Titan.
The long dashed line represents data from (Wilson and Atreya, 2004), the medium dashed line
from (Toublanc et al., 1995), the dotted line from (Lara et al., 1996) and the dash-dotted line
from (Lebonnois et al., 2001).
Figure 9. Rate coefficients for the reaction of C4H with C2H4 as a function of temperature,
displayed on a log-log scale. The filled squares show the experimental results obtained in this
work and the bold solid line shows the fit to these data. The other dashed lines represent
equations used for this reaction in various photochemical models of the atmosphere of Titan.
The long dashed line represents data from (Wilson and Atreya, 2004), the medium dashed line
from (Toublanc et al., 1995) and the dotted line from (Lara et al., 1996).
Figure 10. Relative abundances of C2H2, C2H4, C2H6, CH3C2H and C3H8 with respect to CH4
as a function of altitude in the atmosphere of Titan. Data in the stratosphere are taken from
(Flasar et al., 2005) and (Vinatier et al., 2007) (flyby Tb only). Between 600 and 1000 km,
data are from (Shemansky et al., 2005) and at 1200 km they are derived from (Waite et al.,
2005).
Figure 11. Characteristic reaction time CH4 of the reaction C4H + CH4 relative to the
characteristic reaction time X of the reaction C4H + X with X= C2H2, C2H4, C2H6, CH3C2H
and C3H8 as a function of altitude in the atmosphere of Titan. Lines between data are added
only for clarity.
- 32 -
1.0
0.5
0.0
-0.5
-1.0
LIF signal (arb. units)
residual
FIGURE 1 Berteloite et al.
10
8
6
4
2
0
0
100
200
300
delay time ( sec)
- 33 -
400
500
FIGURE 2 Berteloite et al.
k1st (104 s-1)
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
[C2H6] (1014 molecule cm-3)
- 34 -
FIGURE 3 Berteloite et al.
L M
J
D
intensity (arb. units)
F
E
observed
H
simulated
P
L
K
G
O
24200
W
V
Q
M
W
U
S
R T
N
V
HI
B
A C
24000
F
ST
R
O
I
J
D
E
K
G
U
N
P
24400
24600
-1
wavenumber (cm )
- 35 -
Q
24800
25000
FIGURE 4 Berteloite et al.
R(N’’)
intensity (arb. units)
0 1234567
P(N’’)
23
22
21
20
19
18
17 16 15 14
13 12 11 10 9
8 7
6 5 4 3 2 1
observed
simulated
24476
24478
24480
24482
24484
24486
24488
-1
wavenumber (cm )
- 36 -
24490
24492
24494
FIGURE 5 Berteloite et al.
rate coefficient (cm3 molec-1 s-1)
10-11
10-12
10-13
10-14
10-15
10
100
temperature (K)
- 37 -
FIGURE 6 Berteloite et al.
rate coefficient (cm3 molec-1 s-1)
10-9
10-10
10-11
10-12
10-13
10
100
temperature (K)
- 38 -
rate coefficient (cm3 molec-1 s-1)
FIGURE 7 Berteloite et al.
10-9
10-10
10-11
10
100
temperature (K)
- 39 -
rate coefficient (cm3 molec-1 s-1)
FIGURE 8 Berteloite et al.
10-9
10-10
10-11
10-12
10-13
10
100
temperature (K)
- 40 -
FIGURE 9 Berteloite et al.
rate coefficient (cm3 molec-1 s-1)
10-9
10-10
10-11
10-12
10-13
10
100
temperature (K)
- 41 -
FIGURE 10 Berteloite et al.
1400
1200
altitude (km)
1000
800
C2H2
C2H4
C2H6
C3H8
CH3C2H
600
400
200
0
10-7
10-6
10-5
10-4
10-3
10-2
abundance of hydrocarbons relative to CH4
- 42 -
10-1
FIGURE 11 Berteloite et al.
1400
CH4/ X
1200
=1
C2 H 2
C2 H 4
altitude (km)
1000
800
C2 H 6
C3 H 8
CH3C2H
600
400
200
0
10-4
10-3
10-2
10-1
CH4/
Figure ***, Berteloite et al.
- 43 -
X
100
101